Kim will move south when the order goes out to evacuate Seoul...which will be impossible to do anyway.
It isn't so much as an order to 'move south' as it is to activate the 10,000 artillery tubes.
the DPRK artillery/seoul situation is definitely a mexican standoff; presumably that was part of the intention in its construction and that alone may have prevented any US military action in 94 and more recently.
I don't see a situation ROK can ever agree to support initiating action against DPRK given this, and DPRK is apparently smart enough to not actually do anything that will provoke a real response while they continue their nuclear program.
The only scenario I can imagine where ROK's views on this are summarily ignored is if DPRK is caught exporting a nuke, or a DPRK-origin nuke (or actually any nuke from anyone) is used by a proxy or terrorist org.